How do I draw a solid line when texture painting?
It's hard to say without seeing it, but smoothness will be based upon number of vertices and size of UV map.  

So subdividing your model may help, and possibly setting shading to smooth, but more likely than not increasing the UV texture size will be your best bet.  

It generally defaults to 1024x1024, but when you draw a thin line, those pixels get stretched over the surface of your model, so resolution can make a big difference.   

For broad strokes, small maps are OK... but for fine details, you need more pixels.  Try 2048x2048, or possibly more, especially if your model is large, or you need even more detail.